document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=707037>Question 707037</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Distance between ships: At noon, Ship A is 45 miles due south of Ship B and is sailing north at a rate of 8 miles per hour. Ship B is sailing east at a rate of 6 miles per hour. Write the distance (d) between ships as a function of the time (t), where t=0 represents noon. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435529 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=435529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance between ships: At noon,<BR>\n" );
document.write( " Ship A is 45 miles due south of Ship B and is sailing north at a rate of 8 miles per hour.<BR>\n" );
document.write( " Ship B is sailing east at a rate of 6 miles per hour.<BR>\n" );
document.write( " Write the distance (d) between ships as a function of the time (t), where t=0 represents noon.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The is a Pythagoras problem; d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where:<BR>\n" );
document.write( "a = 6t (distance east)<BR>\n" );
document.write( "b = (45-8t); distance north<BR>\n" );
document.write( "d = distance between the two ships<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Ref point, is the starting point of b when t=0 they are 45 mi apart<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%286t%29%5E2+%2B+%2845-8t%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%286t%29%5E2+%2B+%2845-8t%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "FOIL (45-8t)(45-8t)<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836t%5E2+%2B+2025-720t%2B64t%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2836t%5E2+%2B+2025-720t%2B64t%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28100t%5E2-720t%2B2025%29 ALIGN=MIDDLE  ALT=\"sqrt%28100t%5E2-720t%2B2025%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Graphically, time on the x axis, distance on the y axis<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+20%2C+-20%2C+200%2C+sqrt%28100x%5E2-720x%2B2025%29%2C+107%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+20%2C+-20%2C+200%2C+sqrt%28100x%5E2-720x%2B2025%29%2C+107%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see after 14 hrs, they are about 107 mi apart (green line) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );